Wild singularities of translation surfaces

Joshua Bowman (SUNY Stony Brook)

Abstract: Translation surfaces arise naturally in many dynamical, geometric, and algebraic contexts. Cone-type singularities have played a crucial role in the classical theory of compact translation surfaces. For a non-compact surface, singularities appear as points of the metric completion, and the behavior of the surface near such points can be extremely complicated. We introduce an affine invariant for these singularities in a way that naturally extends the tangent bundle of the surface, and we use this invariant to distinguish among several recently-discovered classes of translation surfaces having the same (infinite) topological type.